[stable32] fix(settings): Improve mail test error handling and logging

[backportbot[bot]]

Backport of #56862

Warning, This backport's changes differ from the original and might be incomplete ⚠️

Todo

• [ ] Review and resolve any conflicts
• [ ] Amend HEAD commit to remove the line stating to skip CI

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Learn more about backports at https://docs.nextcloud.com/server/stable/go.php?to=developer-backports.

[szaimen]

/compile